CN114460605A - Anti-interference method for navigation receiver - Google Patents

Anti-interference method for navigation receiver Download PDF

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CN114460605A
CN114460605A CN202011246556.0A CN202011246556A CN114460605A CN 114460605 A CN114460605 A CN 114460605A CN 202011246556 A CN202011246556 A CN 202011246556A CN 114460605 A CN114460605 A CN 114460605A
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interference
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array
vector
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张柏华
汤加跃
刘俊秀
王令欢
邓一鹗
苏琦
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Xi'an Kaiyang Microelectronic Co ltd
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Xi'an Kaiyang Microelectronic Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/01—Satellite radio beacon positioning systems transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/13—Receivers
    • G01S19/21—Interference related issues ; Issues related to cross-correlation, spoofing or other methods of denial of service

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Abstract

The invention provides an anti-interference method of a navigation receiver, which comprises the following steps: respectively carrying out space-time self-adaptive anti-interference processing on each digital beam by adopting a blind digital multi-beam forming technology; performing space-time null broadening processing on each digital beam to obtain a data covariance matrix after null broadening; and performing signal distortion processing to correct the guide vector of the target satellite. The method can effectively improve the degree of freedom of interference resistance, avoid navigation signal distortion, effectively cope with high dynamic environment and various non-ideal factors (array error, cross coupling, channel amplitude inconsistency and the like), and obviously improve the gains of different satellites, thereby obviously improving the working robustness and navigation positioning precision of the satellite navigation receiver in a complex environment.

Description

Anti-interference method for navigation receiver
Technical Field
The invention belongs to the technical field of satellite navigation, and particularly relates to an anti-interference method for a navigation receiver.
Background
Satellite navigation can provide all-weather, full-time and continuous high-precision three-dimensional position, three-dimensional speed and time information for users on land, sea and space, has incomparable advantages of other navigation modes, and is widely applied to various fields of social life in recent years, particularly military. However, since the satellite is approximately 20000km from the earth's surface, the satellite signal received by the satellite navigation receiver is very weak, only about-160 dBW, and 20-30dB weaker than the thermal noise of the receiver. Therefore, the satellite navigation signal is easily affected by the interference, so that the satellite navigation receiver cannot perform the function of accurate positioning. Improving the anti-interference capability of a satellite navigation system has become the core of a new generation of satellite navigation systems.
In an actual anti-interference system of the satellite navigation receiver, the satellite navigation receiver has limited resources, and the scale of an anti-interference antenna array cannot be large. In recent years, many researches on anti-interference technologies of satellite navigation systems are conducted at home and abroad, an Adaptive filtering method based on array signal Processing is a common anti-interference method at present, and particularly, Space Time Adaptive Processing (STAP) can greatly improve the anti-interference freedom of the system without increasing the number of array elements, so that the method becomes a development trend of the anti-interference technology of satellite navigation, and has important significance for a small-array satellite navigation receiver.
However, in practice, a navigation receiver faces a complex electromagnetic environment, various interferences are intentional and unintentional, interference patterns are various, high dynamics may exist in the navigation receiver and an interference platform, a receiving array may have various non-ideal factors (array errors, mutual coupling, channel amplitude inconsistency and the like), and the distribution azimuth of satellites and the azimuth of the interferences have randomness. Meanwhile, since the STAP adds a delay time signal, applying the conventional STAP will cause serious signal distortion, resulting in unacceptable positioning errors.
Disclosure of Invention
In view of the above, the present invention provides an anti-interference method for a navigation receiver to solve the deficiencies of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
an anti-interference method for a navigation receiver comprises the following steps:
respectively carrying out space-time self-adaptive anti-interference processing on each digital beam by adopting a blind digital multi-beam forming technology;
performing space-time null broadening processing on each digital beam to obtain a data covariance matrix after null broadening;
and performing signal distortion processing to correct the guide vector of the target satellite.
Further, the performing space-time adaptive anti-interference processing on each digital beam by using a blind digital multi-beam forming technology specifically comprises:
respectively aligning different digital beams to different satellites to control the gain loss of each satellite within a preset range; then, respectively carrying out space-time adaptive anti-interference processing on each digital beam, and finally fusing satellites of all digital beams to obtain all satellite conditions; the space-time self-adaptive anti-interference processing adopts the following form: the number of the array elements of the space-time self-adaptive anti-interference array is N, and each array element comprises K delay sampling units; its optimal processor can be described as a mathematical optimization problem as follows:
Figure BDA0002770218770000021
where W represents a weight vector of NK × 1 dimension:
W＝[w11,w12,…,w1K,w21,…,w2K,…,wnk,…,wNK]T
R＝E[XXH]representing a NK x NK dimensional covariance matrix, A, formed by the receiving array dataSIs a space-time two-dimensional steering vector (NK multiplied by 1).
Considering a narrow-band equidistant linear array, the space-time signal vector received by the array can be expressed as:
Figure BDA0002770218770000022
wherein X ═ X11,…,xN1,x12…,xN2,…,x1K…,xNK]TIs an arrayA received space-time data vector; a. theSSpace-time steering vector, X, representing satellite navigation signalss＝[Xs0,…,Xs(K-1)]TRepresenting K delayed satellite signal vectors;
Figure BDA0002770218770000023
is a matrix of NK x K order, wherein IK×KRepresenting a K x K identity matrix,
Figure BDA0002770218770000024
is the product of Kronecker;
Figure BDA0002770218770000031
is the space domain guide vector of the navigation signal, d represents the array element spacing, theta0Representing the included angle between the satellite signal and the array normal line, and lambda represents the carrier wavelength; j. the design is a squarepNKx 1-dimensional vector for representing p-th interference signal and its dispersive multi-path interference
Ji＝[ji1(0),…,jiN(0),ji1(1),…,jiN(1),…,ji1(K),…,jiN(K)]T
ApSpace-time two-dimensional steering vector (NK K) representing the p-th interference
Figure BDA0002770218770000032
Wherein the content of the first and second substances,
Figure BDA0002770218770000033
is the product of Kronecker;
Figure BDA0002770218770000034
wherein, thetapFor disturbing the incident direction and array methodThe angle of the direction is included. n (t) is additive white gaussian noise and is uncorrelated with satellite navigation signals and interference.
Weight vector W of space-time two-dimensional optimal processor can be obtained by utilizing Lagrange multiplier methodoptComprises the following steps:
Wopt＝μR-1AS
wherein, mu is 1/(A)S HR-1AS) Is a constant.
At this time, the array output after STAP anti-interference is
Figure BDA0002770218770000035
Further, the obtaining of the data covariance matrix after null broadening by performing space-time null broadening processing on each digital beam specifically includes:
obtaining a covariance matrix of the array received signals:
Figure BDA0002770218770000036
wherein R isSCovariance matrix, r, representing satellite navigation signalspIs the power of the p-th interfering signal, σ2For noise power, I denotes an identity matrix.
Assuming that there is a perturbation in the angle of incidence of the disturbance
Figure BDA0002770218770000037
And, the disturbance Δ θpObedience mean 0 and variance
Figure BDA0002770218770000038
Normal distribution of
Δθp∈N(0,σp)
In this case, the interference covariance matrix in the presence of disturbance can be obtained
Figure BDA0002770218770000041
Has the following form
Figure BDA0002770218770000042
Wherein the content of the first and second substances,
Figure BDA00027702187700000418
representing a Hadamard product, matrix
Figure BDA0002770218770000043
Is composed of
Figure BDA0002770218770000044
The matrix T essentially acts to expand the direction of the incoming disturbance, by which the influence of the disturbance in the direction of the disturbance is taken into account
Figure BDA0002770218770000045
By
Figure BDA0002770218770000046
The obtained self-adaptive weight
Figure BDA0002770218770000047
Wide nulls can be formed in the interference direction. At this time
Figure BDA0002770218770000048
Wherein the content of the first and second substances,
Figure BDA0002770218770000049
is a constant number, A0The steering vector representing the target satellite, the width of the null being defined by σpAnd (6) determining.
Further, the signal distortion processing and the correction of the steering vector of the target satellite specifically include:
the output of the target satellite signal after space-time self-adaptive null-steering widening anti-interference processing is
Figure BDA00027702187700000410
At this time
Figure BDA00027702187700000411
Is a vector, set
Figure BDA00027702187700000412
Modifying an optimal processor to
Figure BDA00027702187700000413
Equivalently, orthogonal constraint is added to the delayed signals, the influence of different time delay signals on the final synthesized signal can be eliminated, h is 10 … 0, and the optimal weight obtained by solving is in the form of
Figure BDA00027702187700000414
According to the constraint condition, can obtain
Figure BDA00027702187700000415
Can be obtained by finishing
Figure BDA00027702187700000416
At this time, the corrected guide vector a can be obtained0' is an NK x 1-dimensional vector
Figure BDA00027702187700000417
Wherein μ' is a constant
Figure BDA0002770218770000051
Wherein, represents Moore-Penrose generalized inverse.
Since μ 'is constant, it has no influence on the anti-interference effect, and μ' can be made equal to 1, and the final weight calculation formula is modified as follows:
Figure BDA0002770218770000052
at this time, the processed output of each digital beam is:
Figure BDA0002770218770000053
wherein, for digital beams with different directions, A thereof0The same goes for the' same.
The anti-interference method for the navigation receiver is provided based on the complex environment and various non-ideal factors (array error, mutual coupling, channel amplitude inconsistency and the like) faced in practice, and the working robustness and the positioning accuracy of the navigation receiver can be effectively improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of an anti-jamming method for a navigation receiver according to an embodiment of the present invention;
FIG. 2 is a structure diagram of space-time adaptive anti-interference;
FIG. 3 is a captured result of a conventional space-time adaptive processing method;
fig. 4 is a code acquisition result of a conventional space-time adaptive processing method;
FIG. 5 is a Doppler acquisition result of a conventional space-time adaptive processing method;
FIG. 6 is a diagram illustrating an acquisition result of an anti-interference method for a navigation receiver according to an embodiment of the present invention;
fig. 7 is a code acquisition result of an anti-interference method for a navigation receiver according to an embodiment of the present invention;
fig. 8 is a doppler acquisition result of the anti-interference method for the navigation receiver according to the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the present invention provides an anti-interference method for a navigation receiver, which includes the following steps:
and S101, respectively carrying out space-time adaptive anti-interference processing on each digital beam by adopting a blind digital multi-beam forming technology.
Because the number of satellites is large, the distribution is random, the interference is often unknown, when the interference exists, normal acquisition and tracking cannot be performed, the specific orientation of the satellite cannot be acquired, and at the moment, if the interference can be removed effectively only by adopting an anti-interference technology, the gains of different satellites cannot be guaranteed. Signal attenuation for many satellites tends to exceed 10 dB. If digital multiple beams are available, and different digital beams are directed to different satellites, the maximum gain can be achieved for different satellites. As a compromise, it can be considered that a plurality of receiving digital beams are uniformly formed at different directions at the same time, and taking a 4 × 4 area array as an example, the 3dB beam width is about 30 °, at this time, 8 beams uniformly distributed can be formed in the whole space, so that the coverage of the whole space domain can be completed, and the gain loss of each satellite is controlled within 3 dB. And then, each digital beam is subjected to subsequent space-time adaptive anti-interference processing, and finally, satellites of all digital beams are fused, so that all satellite conditions can be obtained.
Space-Time Adaptive Processing (STAP) is a structure that one-dimensional spatial filtering is generalized to a two-dimensional domain of Time and Space to form Space-Time two-dimensional Processing. Brenan firstly proposes the idea of space-time two-dimensional processing, and in the earliest application, a space-time two-dimensional processing adaptive structure is derived by a airborne radar according to the maximum likelihood ratio theory under a model that a gaussian clutter background frame confirms signals (namely, the doppler frequency and the space angle of a target are known), and the space-time two-dimensional processing adaptive structure is called as an optimal processor. STAP theory and technology has grown mature and progressively engineered over several decades of efforts by researchers. Currently, the STAP technology is widely applied to the fields of radar, navigation, sonar, communication and the like.
The structure of the space-time self-adaptive anti-interference is shown in the attached figure 2, wherein the number of array elements is N, and each array element comprises K delay sampling units.
A conventional optimization processor can be described as a mathematical optimization problem as follows:
Figure BDA0002770218770000061
where W represents a weight vector of NK × 1 dimension:
W＝[w11,w12,…,w1K,w21,…,w2K,…,wnk,…,wNK]T (2)
R＝E[XXH]representing a NK x NK dimensional covariance matrix, A, formed by the receiving array dataSIs a space-time two-dimensional steering vector (NK multiplied by 1).
Considering a narrow-band equidistant linear array, the space-time signal vector received by the array can be expressed as:
Figure BDA0002770218770000071
wherein X ═ X11,…,xN1,x12…,xN2,…,x1K…,xNK]TIs a space-time data vector received by the array; a. theSSpace-time steering vector, X, representing satellite navigation signalss＝[Xs0,…,Xs(K-1)]TRepresenting K delayed satellite signal vectors;
Figure BDA0002770218770000072
is a matrix of NK x K order, wherein IK×KRepresenting a K x K identity matrix,
Figure BDA0002770218770000073
is the product of Kronecker;
Figure BDA0002770218770000074
is the space domain guide vector of the navigation signal, d represents the array element distance, theta0Representing the included angle between the satellite signal and the array normal line, and lambda represents the carrier wavelength; j. the design is a squarepNKx 1-dimensional vector for representing p-th interference signal and its dispersive multi-path interference
Ji＝[ji1(0),…,jiN(0),ji1(1),…,jiN(1),…,ji1(K),…,jiN(K)]T (6)
ApSpace-time two-dimensional steering vector (NK K) representing the p-th interference
Figure BDA0002770218770000075
Wherein the content of the first and second substances,
Figure BDA0002770218770000076
is the product of Kronecker;
Figure BDA0002770218770000077
wherein, thetapIs the angle between the interference incidence direction and the array normal. n (t) is additive white gaussian noise and is uncorrelated with satellite navigation signals and interference.
The weight vector W of the space-time two-dimensional optimal processor can be obtained by the Lagrange multiplier method according to the formula (1)optComprises the following steps:
Wopt＝μR-1AS (9)
wherein, mu is 1/(A)S HR-1AS) Is a constant.
At this time, the array output after STAP anti-interference is
Figure BDA0002770218770000078
For a navigation receiver, the number of array elements cannot be too large, space-time adaptive processing is significant, the degree of freedom of interference resistance is greatly increased by combining time domain processing while the degree of freedom of a space domain is not increased, and the possibility of resisting a large amount of dot frequency and narrow-band interference is provided.
And S102, performing space-time null broadening processing on each digital beam to obtain a data covariance matrix after null broadening.
The null obtained by the conventional space-time self-adaptive anti-interference processing is very narrow (usually only about 0.1 degrees), and when various non-ideal factors exist (array element errors, inconsistent amplitudes and phases and under a high dynamic environment), the performance of the space-time self-adaptive anti-interference processing is very lost and even fails. At the moment, a space-time null-steering widening technology is adopted, the null steering is widened to 2-5 degrees, and various non-ideal factors can be effectively dealt with.
The null broadening technology has various implementation schemes, is mainly implemented in a space domain, and the effect is not ideal when the number of array elements is too small (for example, the number of array elements is 4). The scheme is realized by adopting a space-time null broadening scheme.
The covariance matrix of the array received signal can be obtained from equation (3):
Figure BDA0002770218770000081
wherein R isSCovariance matrix, r, representing satellite navigation signalspIs the power of the p-th interfering signal, σ2For noise power, I denotes an identity matrix.
Assuming that there is a perturbation in the angle of incidence of the disturbance
Figure BDA0002770218770000082
And, the disturbance Δ θpObey mean 0 and variance
Figure BDA0002770218770000083
Normal distribution of
Δθp∈N(0,σp) (13)
In this case, the interference covariance matrix in the presence of disturbance can be obtained
Figure BDA0002770218770000084
Has the following form
Figure BDA0002770218770000085
Wherein the content of the first and second substances,
Figure BDA00027702187700000812
representing a Hadamard product, matrix
Figure BDA0002770218770000086
Is composed of
Figure BDA0002770218770000087
The matrix T essentially acts to expand the direction of the incoming disturbance, by which the influence of the disturbance in the direction of the disturbance is taken into account
Figure BDA0002770218770000088
By
Figure BDA0002770218770000089
The obtained self-adaptive weight
Figure BDA00027702187700000810
Wide nulls can be formed in the interference direction. At this time
Figure BDA00027702187700000811
Wherein the content of the first and second substances,
Figure BDA0002770218770000091
is a constant number, A0The steering vector representing the target satellite, the width of the null being σpAnd (6) determining.
And S103, performing signal distortion processing to correct the guide vector of the target satellite.
The output of the target satellite signal after space-time self-adaptive null-steering widening anti-interference processing is
Figure BDA0002770218770000092
At this time
Figure BDA0002770218770000093
Is a vector, set
Figure BDA0002770218770000094
The acquisition and positioning of satellite navigation are mainly realized by the correlation operation of pseudo-random signals, and the cross-correlation function of the received data and known signals is
Figure BDA0002770218770000095
Where p (f) is positive and symmetric about f, the peak of the correlation function is 0 at τ if there is no effect of h (f). However, due to the presence of h (f), the position of the correlation peak is shifted, the main lobe of the correlation peak is widened, and the like, so that the correlation peak cannot be located effectively.
For the navigation signal, since the output is synthesized by signals at different time instants, and the coding of the signals at different time instants is different, the navigation signal is necessarily distorted according to the conventional STAP method.
If we modify equation (1) to
Figure BDA0002770218770000096
The problem of distortion of the navigation signal can be solved well, which is equivalent to adding quadrature constraint to the delayed signal, that is, eliminating the influence of different delay signals on the final composite signal, that is, the signal output of equation (10) does not contain the delay signal. A herein0The same formula (16) is defined, and the calculated weight can not only effectively cancel interference, but also filter the influence of the delay signal on the output. Let h be [ 10 … 0]Solving the equation (18) to obtain the optimal weight value in the form of
Figure BDA0002770218770000097
By substituting the constraint condition of the formula (18) into the formula (19), the expression
Figure BDA0002770218770000098
(20) Formula two-sided right-handed ride A0 HAnd can be finished to obtain
Figure BDA0002770218770000099
At this time, can obtainCorrected guide vector a0' is an NK x 1-dimensional vector
Figure BDA00027702187700000910
Wherein μ' is a constant
Figure BDA0002770218770000101
Wherein, represents Moore-Penrose generalized inverse.
A is solved from the formulas (22) and (23)0' is very difficult and its complexity is high. However, since μ 'is a constant and has no influence on the anti-interference effect, it is possible to set μ' to 1 in calculating the equation (22), and in practice, due to matrix pathological conditions,
Figure BDA0002770218770000102
the inverse of (c) does not necessarily exist and needs to be properly loaded diagonally, which has no effect on the anti-interference effect.
Finally, the final weight calculation formula is obtained by correcting the formula (16) as follows:
Figure BDA0002770218770000103
at this time, the processed output of each digital beam is:
Figure BDA0002770218770000104
wherein, for digital beams with different directions, A thereof0The' is also different.
And (3) MALAB simulation verification:
the following simulation mainly considers the anti-interference performance of the scheme of the invention when various non-ideal factors exist, and simulation parameters are set as follows: the satellite signal is a C/A code, the signal noise is-15 dB, 4 array elements are linear equidistant, the number of delay lines for space-time processing is 4, the single-satellite constraint of LCMV is adopted, the incoming direction of the satellite signal is assumed to be 0 degree (array normal), the interference-to-noise ratio is 40dB, the incoming direction of a broadband suppression interference signal is-30 degrees, the incoming direction of a partial bandwidth interference signal (normalized bandwidth is 0.2-0.6, wherein the whole bandwidth is normalized to be-1 to 1) is 60 degrees, the incoming directions of three narrow-band interferences are respectively-45 degrees, 30 degrees and 45 degrees, the normalized bandwidth is-0.5, -0.1 and 0, the signal received by the array is down-converted to the intermediate frequency of 1.023MHz, the sampling rate is 4.092MHz, and the carrier Doppler frequency is 2.5 KHz. Due to the influence of non-ideal factors, the steering vector is mismatched, and the interference direction is increased by 2 degrees.
As shown in fig. 3 to fig. 5, the correlation peak capturing situation of the conventional space-time adaptive processing method is respectively shown. The traditional space-time adaptive processing method is failed; as shown in fig. 6 to fig. 8, the related peak capturing situations of the proposed technical solutions are respectively given. The solution proposed by the present invention still gives satisfactory results in the presence of a number of non-idealities.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (4)

1. An anti-jamming method for a navigation receiver, comprising:
respectively carrying out space-time self-adaptive anti-interference processing on each digital beam by adopting a blind digital multi-beam forming technology;
performing space-time null broadening processing on each digital beam to obtain a data covariance matrix after null broadening;
and performing signal distortion processing to correct the guide vector of the target satellite.
2. The method according to claim 1, wherein the performing space-time adaptive anti-interference processing on each digital beam separately by using a blind digital multi-beam forming technique specifically comprises:
respectively aligning different digital beams to different satellites to control the gain loss of each satellite within a preset range; then, respectively carrying out space-time adaptive anti-interference processing on each digital beam, and finally fusing satellites of all digital beams to obtain all satellite conditions; the space-time self-adaptive anti-interference processing adopts the following form: the number of array elements of the space-time self-adaptive anti-interference array is N, and each array element comprises K delay sampling units; its optimal processor can be described as a mathematical optimization problem as follows:
Figure FDA0002770218760000011
where W represents a weight vector of NK × 1 dimension:
W＝[w11,w12,…,w1K,w21,…,w2K,…,wnk,…,wNK]T
R＝E[XXH]representing a NK x NK dimensional covariance matrix, A, formed by the receiving array dataSIs a space-time two-dimensional steering vector (NK multiplied by 1).
Considering a narrow-band equidistant linear array, the space-time signal vector received by the array can be expressed as:
Figure FDA0002770218760000012
wherein X ═ X11,…,xN1,x12…,xN2,…,x1K…,xNK]TIs a space-time data vector received by the array; a. theSSpace-time steering vector, X, representing satellite navigation signalss＝[Xs0,…,Xs(K-1)]TRepresenting K delayed satellite signal vectors;
Figure FDA0002770218760000013
is a matrix of order NK K, where IK×KRepresenting a K x K identity matrix,
Figure FDA0002770218760000014
is the product of Kronecker;
Figure FDA0002770218760000015
is the space domain guide vector of the navigation signal, d represents the array element distance, theta0Representing the included angle between the satellite signal and the array normal line, and lambda represents the carrier wavelength; j. the design is a squarepNKx 1-dimensional vector for representing p-th interference signal and its dispersive multi-path interference
Ji＝[ji1(0),…,jiN(0),ji1(1),…,jiN(1),…,ji1(K),…,jiN(K)]T
ApSpace-time two-dimensional steering vector (NK K) representing the p-th interference
Figure FDA0002770218760000021
Wherein the content of the first and second substances,
Figure FDA0002770218760000022
is the product of Kronecker;
Figure FDA0002770218760000023
wherein, thetapIs the angle between the interference incidence direction and the array normal. n (t) is additive white gaussian noise and is uncorrelated with satellite navigation signals and interference.
Weight vector W of space-time two-dimensional optimal processor can be obtained by utilizing Lagrange multiplier methodoptComprises the following steps:
Wopt＝μR-1AS
wherein, mu is 1/(A)S HR-1AS) Is a constant.
At this time, the array output after STAP anti-interference is
Figure FDA0002770218760000024
3. The method of claim 1, wherein the obtaining the data covariance matrix after null broadening by performing space-time null broadening processing on each digital beam specifically comprises:
obtaining a covariance matrix of the array received signals:
Figure FDA0002770218760000025
wherein R isSCovariance matrix, r, representing satellite navigation signalspIs the power of the p-th interfering signal, σ2For noise power, I denotes an identity matrix.
Assuming that there is a disturbance in the incident angle of the disturbance
Figure FDA0002770218760000026
And, the disturbance Δ θpObedience mean 0 and variance
Figure FDA0002770218760000027
Normal distribution of
Δθp∈N(0,σp)
In this case, the interference covariance matrix in the presence of disturbance can be obtained
Figure FDA0002770218760000028
Has the following form
Figure FDA0002770218760000031
Wherein the content of the first and second substances,
Figure FDA0002770218760000032
representing a Hadamard product, matrix
Figure FDA0002770218760000033
Is composed of
Figure FDA0002770218760000034
The matrix T essentially acts to expand the direction of the incoming disturbance, by which the influence of the disturbance in the direction of the disturbance is taken into account
Figure FDA0002770218760000035
By
Figure FDA0002770218760000036
The obtained self-adaptive weight
Figure FDA0002770218760000037
Wide nulls can be formed in the interference direction. At this time
Figure FDA0002770218760000038
Wherein the content of the first and second substances,
Figure FDA0002770218760000039
is a constant number, A0The steering vector representing the target satellite, the width of the null being defined by σpAnd (6) determining.
4. The method of claim 1, wherein the performing signal distortion processing to modify the steering vector of the target satellite specifically comprises:
the output of the target satellite signal after space-time self-adaptive null-steering widening anti-interference processing is
Figure FDA00027702187600000310
At this time
Figure FDA00027702187600000311
Is a vector, set
Figure FDA00027702187600000312
Modifying an optimal processor to
Figure FDA00027702187600000313
Equivalently, orthogonal constraint is added to the delay signals, the influence of different time delay signals on the final composite signal can be eliminated,
let h be [ 10 … 0], the form of solving the obtained optimal weight is
Figure FDA00027702187600000314
According to the constraint conditions, can obtain
Figure FDA00027702187600000315
Can be obtained by finishing
Figure FDA00027702187600000316
At this time, the corrected guide vector a can be obtained0' is an NK x 1-dimensional vector
Figure FDA00027702187600000317
Wherein μ' is a constant
Figure FDA0002770218760000041
Wherein, represents Moore-Penrose generalized inverse.
Since μ 'is constant, it has no influence on the anti-interference effect, and μ' can be made equal to 1, and the final weight calculation formula is modified as follows:
Figure FDA0002770218760000042
at this time, the processed output of each digital beam is:
Figure FDA0002770218760000043
wherein, for digital beams with different directions, A thereof0The' is also different.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115372998A (en) * 2022-08-22 2022-11-22 中国矿业大学 Low-complexity robust wide-linear beam forming method for satellite navigation receiver
CN117348038A (en) * 2023-10-09 2024-01-05 中国矿业大学 Robust space-time self-adaptive processing method for satellite navigation receiver in coherent signal environment

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115372998A (en) * 2022-08-22 2022-11-22 中国矿业大学 Low-complexity robust wide-linear beam forming method for satellite navigation receiver
CN115372998B (en) * 2022-08-22 2023-04-07 中国矿业大学 Low-complexity robust wide-linear beam forming method for satellite navigation receiver
CN117348038A (en) * 2023-10-09 2024-01-05 中国矿业大学 Robust space-time self-adaptive processing method for satellite navigation receiver in coherent signal environment

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